Optical detection of fractional particle number in an atomic Fermi-Dirac gas

We study theoretically a Fermi-Dirac atomic gas in a one-dimensional optical lattice coupled to a coherent electromagnetic field with a topologically nontrivial soliton phase profile. We argue that the resulting fractional eigenvalues of the particle number operator can be detected via light scattering. This could be a truly quantum mechanical measurement of particle number fractionalization in a dilute atomic gas.     

Linear Differential Equations and Logarithmic Derivative Estimates

We prove two sharp inequalities for the growth of solutionsof certain linear differential equations in the unit disk. Forthe proofs of these inequalities, we use the method of successiveapproximations and sharp estimates for the logarithmic derivativesof finite order meromorphic functions in the unit disk. Thesetechniques can also be used to give an alternate proof of awell-known result in the plane. The sharp logarithmic derivativeestimates are a corollary of general estimates, and all theseestimates have independent interest. 2000 Mathematics SubjectClassification 34M10, 30D35.     

Zero separation results for solutions of second order linear differential equations

The oscillation of solutions of f^″+Af=0$f^{″}+Af=0$ is discussed by focusing on four separate situations. In the complex case A$A$ is assumed to be either analytic in the unit disc D$\mathbb{D}$ or entire, while in the real case A$A$ is continuous either on (−1,1)$(-1,1)$ or on (0,∞)$(0,\infty )$. In all situations A$A$ is expected to grow beyond bounds that ensure finite oscillation for all (non-trivial) solutions, and the separation between distinct zeros of solutions is considered.     

Enhanced hydrophobicity of rough polymer surfaces

Molecular dynamics simulations were used to study the effect of periodic roughness of PE and PVC polymer surfaces on the hydrophobicity. Pillars of different lateral dimensions and heights were derived from flat crystalline surfaces, and the results of nanoscale simulations on the structured surfaces were compared with theoretical predictions of the Wenzel and Cassie equations. Hydrophobicity increased on all rough surfaces, but the increase was greater on the structured PE surfaces because of the larger water contact angle on the flat PE surface than the corresponding PVC surface. Equally sized pillar structures on the two polymers resulted in different equilibrium wetting geometries. Composite contacts were observed on rough PE surfaces, and the contact angle increased with decreasing contact area between the solid and the liquid. Opposite results were obtained for rough PVC surfaces; the contact angle increased with the solid-liquid contact area, in agreement with Wenzel's equation. However, the composite contact was observed if the energies of the wetted and composite contacts were almost equal. Good agreement was obtained between the simulated contact angles and equilibrium droplet shapes and the theories but there were also some limitations of the nanoscale simulations.     

The behaviour of cationic NanoFibrillar Cellulose in aqueous media

This paper deals, with cationically modified NanoFibrillar Cellulose (cat NFC), obtained by reacting a dissolving pulp with 2,3-epoxypropyl trimethylammonium chloride (EPTMAC). The cat NFC was thoroughly characterized in terms of morphology and physical properties. The dimensions of individual cellulose nanofibrils were determined by atomic force microscopy (AFM) imaging in water and in air. Fibrils as thin as 0.8–1.2 nm were observed in water. The fibril diameter changed upon drying and the average size was further quantified by image analysis. The experiments showed the importance of characterizing nanocellulosic materials in situ before drying. The fibril size in air was confirmed by cryogenic transmission electron microscopy (cryo-TEM), and it was found to be 2.6–3.0 nm. Smooth ultrathin films of cationic NFC were prepared by spincoating on silica substrates. The effect of electrolyte concentration and pH on swelling of the cationic NFC film was studied using a quartz crystal microbalance with dissipation. The results showed that at pH = 8 the cat NFC film was insensitive to electrolyte changes while at pH = 4.5, the water content of the film decreased with increasing ionic strength. The electrophoretic mobility measurements showed a cationic zeta potential for the cat NFC that decreased at increasing pH, verifying the swelling behaviour.     

Surface functionalization of nanofibrillated cellulose using click-chemistry approach in aqueous media

In the present work, amino functionalized nanofibrillated cellulose (NFC) was prepared using click-chemistry in aqueous reaction conditions. First, reactive azide groups were introduced on the surface of NFC by the etherification of 1-azido-2,3-epoxypropane in alkaline water/isopropanol-mixture at ambient temperature. Then the azide groups were reacted with propargyl amine utilizing copper catalyzed azide-alkyne cycloaddition (CuAAC), leading to pH-responsive 1,2,3-triazole-4-methanamine decorated NFC. The reaction products were characterized using Fourier transform infrared spectroscopy, elemental analysis and X-ray photoelectron spectroscopy. The presence of the attached azide groups was also confirmed by reacting them with 5-(dimethylamino)-N-(2-propyl)-1-naphthalenesulfonamide by CuAAC, yielding highly fluorescent NFC. In addition, atom force microscopy and rheology studies confirmed that the original NFC nanostructure was maintained during the synthesis.     

Photocatalytic degradation of methylene blue in water solution by multilayer TiO2 coating on HDPE

A multilayer photocatalytic TiO₂ coating on a high-density polyethylene (HDPE) disk was found to degrade aqueous methylene blue in a batch reactor study. The TiO₂ coating was fabricated by a low-temperature method using polyurethane resin (PU) as a barrier layer for HDPE and as a binding agent for two TiO₂ layers. Adequate adhesion between the HDPE substrate and PU barrier in aqueous environment was ensured with an oxygen plasma treatment.The photocatalytic effect of immersed TiO₂ coating on the degradation of methylene blue in aqueous solution was monitored by UV–vis spectrometry as a function of UV-illumination time. Samples were allowed to adsorb methylene blue in the dark for 1 h before the UV-degradation experiments were started. The percentages of methylene blue degraded during 6 h UV illumination (λ = 365 nm) varied from 80% to 92%. The degradation followed pseudo-first order reaction kinetics, and the observed rate constants (k_obs) were between 0.27 and 0.43 h⁻¹.     

Intermolecular Interactions and the Adhesion of Oleic Acid

The method presented by Good, van Oss, and Chaudhury was applied to characterize intermolecular interactions and the adhesion of oleic acid to selected model surfaces. Interfacial tensions of oleic acid were on the order 11–12 mJ/m² in aqueous solutions and 31–32 mJ/m² at air. The dispersive contribution to the surface tension of oleic acid against different neutral interfaces was determined to be 24–31 mJ/m² in air. Contact angles of oleic acid on selected hydrophilic and hydrophobic model surfaces were measured both in air and in aqueous solution. Van der Waals (dispersive) interactions determined the wetting properties of oleic acid in air both on nonpolar and basic surfaces. As expected, the adhesion of oleic acid to hydrophilic surfaces was much lower and to hydrophobic surfaces higher in aqueous environment than in air. The adhesion in aqueous environment is mainly governed by the cohesive and adhesive properties of water. It was concluded that the GvOC method in this case was only capable to give qualitative information about Lewis acid-base and van der Waals properties of surfaces and liquids, an important limiting factor being the asymmetry of oleic acid and the common probe liquids (diiodomethane and water).     

Titrimetric methods for the determination of surface and total charge of functionalized nanofibrillated/microfibrillated cellulose (NFC/MFC)

Total and surface charge of three different carboxymethylated nanofibrillated/microfibrillated cellulose (NFC/MFC) samples were investigated by using titrimetric methods (conductometric and polyelectrolyte (PE) titrations). Conductometric titration was found to be suitable method for the NFC total charge measurements when the back titration with HCl was applied. Surface charge measurements of NFC/MFC were conducted by using both indirect and direct PE titrations. The direct PE titration was found to be a more suitable method for the surface charge determination of NFC/MFC whereas the indirect PE titration produced too high surface charge values. This is presumably due to kinetically locked polyelectrolyte conformations on the NFC/MFC surfaces or entrapment of residual polymer after adsorption onto the NFC/MFC gel network. Finally, NFC was propargyl-functionalized and the changes in surface and total charge were successfully monitored and compared to those of propargyl-functionalized pulp. A good correlation between the titrimetric methods and elemental analysis was observed.     

All-cellulose multilayers: long nanofibrils assembled with short nanocrystals

Self-organized multilayer films were formed by sequential addition of oppositely charged cellulose I nanoparticles. The all-cellulosic multilayers were prepared via adsorption of cationicially modified cellulose nanofibrils (cat NFC) and anionic short crystalline cellulose (CNC) at pH 4.5 and pH 8.3. The properties and build-up behavior of layer-by-layer-constructed films were studied with microgravimetry (QCM-D) and the direct surface forces in these systems were explored with colloidal probe microscopy to gain information about the fundamental interplay between cat NFC and anionic CNC. The importance of the first layer on the adsorption of the consecutive layers was demonstrated by comparing pure in situ adsorption in the QCM-D with multilayer films made by spin coating the first cationic NFC layer and then subsequently adsorbing the following layers in situ in the QCM-D chamber. Differences in adsorbed amount and viscoelastic behavior were observed between those two systems. In addition, a significant pH dependence of cat NFC charge was found for both direct surface interactions and layer properties. Moreover the underlying cellulose layer in multilayer film was established to influence the surface forces especially at lower pH, where the cat NFC chains extensions were facilitated and overall charge was affected by the cationic counterpart within the layers. This enhanced understanding the effect of charge and structure on the interaction between these renewable nanoparticles is valuable when designing novel materials based on nanocellulose.